A031688 Numbers k such that the continued fraction for sqrt(k) has odd period and if the last term of the periodic part is deleted the two central terms are both 100.

2501, 123953, 203482, 204385, 206197, 304825, 425273, 568741, 726193, 727898, 734738, 906665, 1119805, 1124041, 1334554, 1341493, 1346129, 1565626, 1568129, 1570634, 1573141, 1578161, 1580674, 1583189, 1590746, 1593269, 1828633, 2126605, 2138285, 2144137

Offset

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..1000

Mathematica

cf100Q[n_]:=Module[{s=Sqrt[n], cf, len}, cf=If[IntegerQ[s], {1, 1}, ContinuedFraction[ s][[2]]]; len=Length[cf]; OddQ[len] && cf[[(len+1)/2]] == 100]; Select[Range[2200000], cf100Q] (* Harvey P. Dale, May 29 2016 *)

Prog

(Python)
from sympy import continued_fraction_periodic
A031688_list = [n for n, s in ((i, continued_fraction_periodic(0, 1, i)[-1]) for i in range(1, 10**5)) if isinstance(s, list) and len(s) % 2 and s[(len(s)-1)//2] == 100] # Chai Wah Wu, Jun 11 2017

Crossrefs

Sequence in context: A235404 A120408 A031778 * A031548 A045216 A205175

Adjacent sequences: A031685 A031686 A031687 * A031689 A031690 A031691

Keyword

nonn

Author

David W. Wilson

Extensions

Definition corrected and terms corrected and extended by Harvey P. Dale, May 29 2016

Status

approved